设x=-2又2分之1,求6x+[(x-2)分之(x) -(x+2)分之(x)]除以(x的4次方-2x的3次方+8x-16)分之(4x)

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设x=-2又2分之1,求6x+[(x-2)分之(x) -(x+2)分之(x)]除以(x的4次方-2x的3次方+8x-16)分之(4x)
设x=-2又2分之1,求6x+[(x-2)分之(x) -(x+2)分之(x)]除以(x的4次方-2x的3次方+8x-16)分之(4x)

设x=-2又2分之1,求6x+[(x-2)分之(x) -(x+2)分之(x)]除以(x的4次方-2x的3次方+8x-16)分之(4x)
数学之美团为你解答
6x + [ x/(x-2) - x/(x+2) ] ÷ [ 4x / (x⁴ - 2x³ +8x - 16) ]
= 6x + 4x / [ (x+2)(x-2) ] ÷ { 4x / [ x³(x-2) + 8(x-2) ] }
= 6x + 4x / [ (x+2)(x-2) ] ÷ { 4x / [ (x³ +8 ) (x - 2) ] }
= 6x + 4x / [ (x+2)(x-2) ] ÷ { 4x / [ (x+2)(x² - 2x +4 )(x - 2) ] }
= 6x + 4x / [ (x+2)(x-2) ] × [ (x+2)(x² - 2x +4 )(x - 2) ] / 4x
= 6x + (x² - 2x +4)
= x² + 4x +4
= (x+2)²
= ( 2又1/2 +2)²
= ( 5/2 +2)²
= 81/4
\

无聊

6x + [ x/(x-2) - x/(x+2) ] ÷ [ 4x / (x⁴ - 2x³ +8x - 16) ]
= 6x + 4x / [ (x+2)(x-2) ] ÷ { 4x / [ x³(x-2) + 8(x-2) ] }
= 6x + 4x / [ (x+2)(x-2) ] ÷ { 4x / [ (x³ +8 ) (x - 2)...

全部展开

6x + [ x/(x-2) - x/(x+2) ] ÷ [ 4x / (x⁴ - 2x³ +8x - 16) ]
= 6x + 4x / [ (x+2)(x-2) ] ÷ { 4x / [ x³(x-2) + 8(x-2) ] }
= 6x + 4x / [ (x+2)(x-2) ] ÷ { 4x / [ (x³ +8 ) (x - 2) ] }
= 6x + 4x / [ (x+2)(x-2) ] ÷ { 4x / [ (x+2)(x² - 2x +4 )(x - 2) ] }
= 6x + 4x / [ (x+2)(x-2) ] × [ (x+2)(x² - 2x +4 )(x - 2) ] / 4x
= 6x + (x² - 2x +4)
= x² + 4x +4
= (x+2)²
( -2又1/2 +2)²
= (-5/2 +2)²
= 1/4

收起

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